Most of the diving on the LA rigs is "bottomless" diving, as there is generally not a well defined bottom to go to, at least not one you can see, and often it is well outside even mxed gas depths.
Absolutely solid buoyancy control, depth sensing, and navigation by piloting are MANDATORY skills for diving these rigs safely. Compasses don't work, since they just point to the nearest leg, and navigating by current direction is not trustworthy since there may be 4 or 5 different layers of water all moving in different directions at different depths.
Needless to say I don't think these rigs are a great place to start out beginning OW divers. To do rigs safely with beginners hit the ones out of Pensacola, Mobile (Gulf Shores or Dauphin Island), or Gulfport. If it was my family I'd lean towards Pensacola or Gulf Shores for a first trip. Diving there is resonable, not over dove as bad as the points farther east, and usually has reasonable vis.
I did a few rigs about 30 miles out of Beaumont 20 years ago that were good, with reasonable vis and a solid bottom. I don't know if anyone is running dive charters out of there now, or if the rigs are still there.
Be aware that once east of The River the farther east you go the worse the good days get, and the better the bad days get. Out of Gulfport vis can be 200' or 2", off Panama City vis is usually 30 to 60 feet. Of course the farther south you go the better it gets, but diving in several hundred feet of water 75 to 100 miles out isn't what I consider a place for newbies.
If doing LA rigs the ones out of Fouchon to Lake Charles will tend to be shallower. If leaving from Venice or Empire rigs in clear water will generally have water depths in 3 or 4 figures, with the first figure not being a 1 until you get to 4 figures. The only advantage for newbies of the Empire and Venice rigs are the run to blue water is much shorter, and the fish are MUCH bigger.
FT